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Shortest Networks on Surfaces

In: Handbook of Combinatorial Optimization

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  • J. F. Weng

    (The University of Melbourne, Department of Mathematics and Statistics)

Abstract

Suppose A = {a l, a 2, ... , a n } is a point set in a metric space M. The shortest network problem asks for a minimum length network S(A) that interconnects all points of A (called terminals), possibly with some additional points to shorten the network. S(A) must be a tree since it cannot contain any cycle for minimality. In the literature this problem is called the Steiner tree problem, and S(A) is called a Steiner minimal tree for A [9]. If no additional points are added, then the network, denoted by T(A), is called a minimal spanning tree on A. Sometimes these networks are simply denoted by S and T if no confusion is caused.

Suggested Citation

  • J. F. Weng, 1998. "Shortest Networks on Surfaces," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 1335-1362, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0303-9_21
    DOI: 10.1007/978-1-4613-0303-9_21
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